Mathematical Model.– Throughout this paper we will consider the Langevin dynamics (REF ) with a harmonic potential \(U(t,x)=\frac{1}{2}q(t)x^2\) , where \(q(t)\)  represents its intensity and constitutes our control variable. The total energy of a particle is the sum of kinetic and potential energies, \( E_t = \frac{1}{2}mv_t^2 + \frac{1}{2}q(t)X_t^2\) . The work and heat exchange at the level of a single particle, \(d\hspace*{-1.00006pt}\bar{}\hspace*{1.99997pt}W_t\)  and \(d\hspace*{-1.00006pt}\bar{}\hspace*{1.99997pt}Q_t\) , respectively, are [1]}
\(d\hspace*{-1.00006pt}\bar{}\hspace*{1.99997pt}W_t &= \frac{1}{2}\dot{q}(t) X_t^2 dt,\\d\hspace*{-1.00006pt}\bar{}\hspace*{1.99997pt}Q_t &= -\gamma v_t^2 {\color {black}{dt}} + \frac{\gamma k_B T(t)}{m} dt + \sqrt{2\gamma k_BT(t)} v_t dB_t.\) 
